The Icelandic Deep Drilling Project (IDDP) is a research program designed to evaluate improvements in the efficiency and economics of geothermal energy systems by harnessing Deep Unconventional Geothermal Resources (DUGR). The goal is to generate electricity from natural supercritical hydrous geofluids from depths of around 3.5 to 5 km and temperatures of 450-600°C. At that depth, the pressure and temperature of pure water exceed the critical point of 374.15°C and 221.2 bars, which means that only a single phase fluid exists. In order to drill into the target zone of supercritical geofluids, one of the main challenges is to deal with high temperatures and pressures during the drilling and well completion processes. Because of the great uncertainties in this project a detailed risk assessment and contingency plan is necessary.This thesis describes major geological and technical problems, in terms of drilling, in such a high temperature and pressure environment, with emphasis on the geo-engineering part of the drilling process and well completion. The natural geological risks arising from volcanic and seismic activity, as well as meeting sufficient permeable zones, are considered to be relatively minor factors when compared to the well completion process due to their low probability. The main risks are assessed in the hazard of underground pressure blowouts, meeting circulation loss zones and material failures due to the high temperature environment. In addition borehole failure, formation fracturing, cement and casing failure as well as problems during coring operations are deemed to be likely, but by applying the appropriate techniques as well as mitigation and counteractive measures, discussed in this thesis, most of these risks can be reduced or prevented.